Find the change in height of the leaning tower

The Leaning Tower of Pisa is 56.84 meters long. In the 1990’s, engineers restored the building so that angle y changed from 5.5° to 3.99°.  To the nearest hundredth of a meter, how much did the restoration change the height of the Leaning Tower of Pisa?

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The height of the tower is adjacent to ∠ y.
The length of the tower is the hypotenuse of the triangle created.

adjacent
——————— = cosine of ∠y
hypotenuse


Let x be the height of the tower  (the adjacent side to angle y).

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​If the angle was 5.5°,

      x
——————  =  cos 5.5°
   56.84

      x
—————— ≈ 0.995396198367   {evaluated cosine of 5.5°}
  56.84

x  ≈  56.58    {multiplied each side by 56.84}



If the angle was 3.99°,

      x
—————— = cos 3.99°
   56.84

      x
—————— ≈ 0.997576209867   {evaluated cosine of 3.99°}
   56.84

x ≈ 56.7   {multiplied each side by 56.84}


Change in height
= 56.7 - 56.58
= 0.12 m

Ask Algebra House
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